DEVELOPMENT OF A VIRTUAL NUMERICAL LABORATORY FOR EARTH-PLANETARY FLUID DYNAMICS USING SPECTRAL METHODS

本研究的目的是在互联网上建立一个虚拟的地球行星流体“数值实验室”。在必要的谱方法发展方面，提出了一种新的圆盘上浅水方程的谱方法，详细内容发表为两篇原创论文。该方法采用雅可比多项式作为展开的基础，避免了采用极坐标时常出现的原点奇异性。该方法的新颖之处在于直接展开向量场。此外，还开发了一维/二维无限域的新光谱方法，目前正在准备论文。利用该技术，对浅水系统中不稳定射流的重力波辐射进行了数值实验。对引力波的参数依赖性进行了研究，并作为论文提交。开发的数值库免费发布于http://www.gfd-dennou.org/arch/ispack/ispack-0.62beta.tar.gz。此外，根据数值库的开发经验，出版了第一本日文谱方法教科书。为了提供虚拟实验室环境，新建了一个公司的web服务器，该服务器不仅保存了一系列已开发的地球行星流体计算光谱模型的源代码和解释，而且还保存了一个典型练习的执行结果。内容免费发布于http://www.gfd-dennou.org/arch/spmodel/。

The research was accomplished aiming to construct a virtual "numerical laboratory" of earth planetary fluid in the Internet.As for the development of necessary spectral methods, a new spectral method was developed for shallow water equations on a disk, the details of which are published as two original papers. This method uses Jacobi polynomials as a basis of expansion to avoid the singularity at the origin which often appears when the polar coordinate is adopted. The novelty of the method is in expanding vector fields directly.In addition, new spectral methods for 1d/2d infinite domains are developed, and the paper is being prepared now. By using this technique, numerical experiments of gravity wave radiation from an unstable jet in a shallow water system are conducted. The parameter dependency of the gravity waves are examined, and it is contributing as a submitted paper. The developed numerical library is distributed freely as http://www.gfd-dennou.org/arch/ispack/ispack-0.62beta.tar.gz. Furthermore, the first textbook for spectral methods in Japanese is published based on the experiences in the development of the numerical library.To provide the virtual laboratory environment, a firm web server is newly started up, which maintains not only the source code of a series of developed spectral models for the earth planetary fluid calculation and the explanation, but also the execution result of a typical exercise. The contents are distributed freely as http://www.gfd-dennou.org/arch/spmodel/.